I shoot RAW mostly, so I guess that wouldn't be too much of a difference I guess.
After going to a store and experimenting, I seem to like the D750 more than the D610 in terms of feel, layout and controls... but then the D750 is more expensive, naturally that happens haha.
There are a few SW features which are nice on the D750 and some focus improvements that are not on the D6x0.. but you lost me when you said differences in feel, layout and controls. What specific one's are you talking about?
Mainly ergonomics.
The tilting LCD, extra battery life, and I seem to like the placements of buttons on the D750 better.
I do like the Wi-Fi function as an extra.
However, I think I'll just get a D6x0 and a battery grip.. as I like battery grips and I'm inseparable from them...
here is my list of things I would have liked as an improvement on the D6x0 and other things that you listed that the D750 has.
You can do the same thing on the D600 using an add in wifi adapter. However, I have found the app and feature set of Nikon wifi across the board to be quite bad. Regardless of which model body. In short, it been a disappointed I don't use it. I hope this changes with their upcoming switch to Snapbridge. Have a look at the reviews of the wifi.. especially if you will be using an app on your smart phone. take a close look before you value this too much.
I was not aware of any significant difference in battery life.
Most people find that the D6x0 mis-focuses in artificial lighting. i.e. typical indoor photography. I can confirm that it does. However, it can be fixed. Recently Nikon did some kind of magic on mine and now I can get accurate focus with different kinds of light. However, it did cost me $155 for them to fix plus shipping the camera to them. So budget for that if you intend to shot it anything other than mid time daylight. Oh.. yeah.. golden hour throws it off too with the warm light.
If you wear glasses, you really should handle the camera in landscape orientation ahead of time and check that all of the corners are clear to you with your glasses on. Same goes for the D750. Put the camera up to white wall or sky and see if it feels comfortable to you and you can see all the corners at once without read adjusting your position. Also make sure its comfortable as the viewfinder is actually recessed into the body, tilting my head at an awkward angle more than pro bodies. The net result, are two darker corners and uncomfortable to use compared to the pro bodies. If you have a store near you, go compare between D6x0, D750 and a pro body like D8x0, D4s and if they have used D700.
It has no way to do quick one button 100% review of the focus area to check focus. On the higher end bodies you can simply hit the "OK" button in the middle of my multi-selector and get a 100% view of where you focused.
The flash x-sync is limited to 1/200. If you want to overpower daylight with your flash, every little bit more helps.
No way to lock the aperture dial and shutter dials. I often bump these and its kind of annoying to keep inspecting settings between shots to make sure they didn't move.
Tends to need cleaning of the sensor more than my other cameras. However, that said all camera need cleaning eventually. If you have a D600, the service is free for life but you need to pay for shipping to Nikon. Could be a pro or could be a con. Depends on your point of view.
Other than that its a great camera. Enjoy.